Analysis of Caputo-Type Non-Linear Fractional Differential Equations and Their Ulam–Hyers Stability.

Girgin, Ekber; Büyükkaya, Abdurrahman; Kuru, Neslihan Kaplan; Younis, Mudasir; Öztürk, Mahpeyker

This study presents two novel frameworks, termed a quasi-modular b-metric space and a non-Archimedean quasi-modular b-metric space, and various topological properties are provided. Using comparison and simulation functions, this paper rigorously proves several fixed point theorems in the non-Archimedean quasi-modular b-metric space. As a useful application, it also establishes Ulam–Hyers stability for the fixed point problem. Finally, this study concludes with a unique solution to a non-linear fractional differential equation, making a substantial contribution to the discipline.

NONLINEAR differential equations; FRACTIONAL differential equations; TOPOLOGICAL property; NONLINEAR analysis; FIXED point theory

Fractal & Fractional, 2024, Vol 8, Issue 10, p558

2504-3110

Academic Journal

10.3390/fractalfract8100558